Formula:KLS:01.15:11

<< Formula:KLS:01.15:10

formula in The q-derivative and q-integral

Formula:KLS:01.15:12 >>

${\displaystyle{\displaystyle{\displaystyle\int_{a}^{b}f(t)\,d_{q}t=b(1-q)\sum_{n=0}^{\infty}f(bq^{n})q^{n}-a(1-q)\sum_{n=0}^{\infty}f(aq^{n})q^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle 0<q<1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation in Section 1.15 of KLS.

URL links

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<< Formula:KLS:01.15:10

formula in The q-derivative and q-integral

Formula:KLS:01.15:12 >>